CN110083179A - A kind of predetermined time multi-agent system consistency tracking and controlling method - Google Patents
A kind of predetermined time multi-agent system consistency tracking and controlling method Download PDFInfo
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Abstract
The present invention relates to a kind of predetermined time multi-agent system consistency tracking and controlling methods, comprising: design predetermined time distribution observer estimates tracking error in the given time；According to the predetermined time, distribution observer parameter is determined；Predetermined time non-singular terminal sliding formwork consistency control protocol is designed, follower's multi-agent system is enable to track the track of leader's multiagent system in the given time；It determines the continuity and differentiability that can guarantee sliding-mode surface, eliminates the controller parameter of control singularity；The distributed observer proposed and consistency control protocol are deployed on each follower's intelligent body, realize the tracking of predetermined time consistency.When existing fixation compared with coherence scheme, the method for the present invention can obtain the convergence time estimation of lower conservative, this also contributes to the conservative for reducing controller design.Therefore, the method for the present invention above shows wide application prospect in the multi-agent system application more demanding to control precision and convergence time.
Description
Technical field
The present invention relates to multi-agent system Collaborative Control technical fields, in particular to a kind of predetermined time multiple agent system
System consistency tracking and controlling method.
Background technique
In recent years, the control of multi-agent system distributed collaboration has obtained commonly used, including network in every field
Change robot manipulator coordinated control, robotic tracking and deployment, unmanned systems are formed into columns and microgrid energy management.Distributed collaboration
One basic problem of control is that Design consistency agreement is realized all intelligent bodies by local communication and synchronized, the problem
Referred to as consistency problem.Whether there is or not leaders can be divided into again according in system for consistency problem: without leader's consistency problem with it is consistent
Property tracking problem.Without leader's consistency refer to all intelligent bodies converge to the average value or first state of value of original state weighting it is flat
Mean value.Consistency, which follows, refers to all tracks for following and leading on intelligent volume tracing, and the target of group can pass through the shape of leader
State is specified.Therefore, compared with without leader's consistency, consistency tracking improves the flexibility of target population realization, by science
The extensive concern on boundary and industry.
The key for solving consistency tracking problem is Design consistency control protocol.Evaluate designed consistency control association
One important performance indicator of view is convergence rate.Pertinent literature shows that promoting algebraic connectivity helps to promote consistency control
The convergence rate of agreement processed.This excites researcher and accelerates convergence by design best initial weights or the better communication topology of selection
Speed.However, these methods be only able to achieve it is progressive consistent, it means that multiagent system can not be realized accurately in finite time
Consistency.Consistency can realize that multi-agent system is accurately consistent in finite time when limited.With it is progressive it is consistent compared with,
Unanimously there is higher consistency precision, faster convergence rate and to interfering and do not know stronger robustness when limited.It is right
It is consistent when people prefer to realize limited in certain pairs of control precision and the demanding application of convergence time.Therefore, it studies
Consistency control protocol when personnel spend great effort design limited, homogeneity method, adding one power integrator method and terminal sliding mode
Method is for consistency control protocol when designing limited.However, the convergence time of consistency control protocol takes when existing limited
Certainly in the initial value of intelligent body.However, the initial value of practical multiagent system is difficult to obtain, this brings difficulty to estimation convergence time.
In addition, with initial value level off to it is infinite, the consistency time also level off to it is infinite, which prevent it is limited when consistency be applied to initial value
Very big multi-agent system.
The performance of consistency protocol, sets Gu timing stability is introduced in consistency control protocol when to promote existing limited
In meter.Gu timing consistency has, attracting characteristic --- the convergence time upper bound is a constant unrelated with original state,
This facilitates controller design and stablizes time Estimate, so that solid timing controlled is suitably applied with the stringent convergence time upper bound
Application, for example, electric power system control and far-end operation system control.Gu timing controlled agreement has been used for realizing band
There are undirected communication topology, the consistency of oriented communication topology and switching communication topology multi-agent system.However, existing result
There are two main problems.Firstly, the convergence time upper bound obtained by stability analysis is very conservative.Secondly, when fixed
The upper bound of consistency protocol convergence time is the complicated function of control parameter, without aobvious between adjustment parameter and the stable time upper bound
Formula relationship.In order to overcome the above problem, need to develop predetermined time stability contorting.Compared with stability contorting when fixed, pre- timing
Between stability contorting have following two advantage: firstly, the convergence time upper bound of predetermined time stability contorting be equal to controller adjusting
Parameter, this facilitate that controller design is to meet the requirement of stable time；Secondly, the adjustment parameter of controller is to stablize the time most
The small upper bound, so as to avoid the excessive estimation to convergence time boundary.By predetermined time stability expand to solve consistency with
Track problem needs to solve the problems, such as two challenging problem in science --- predetermined time observation and control singularity problem.It arrives
So far, there are no documents to propose predetermined time consistency control protocol.Realize the predetermined time lead-follow consistency to help
In determining control protocol gain and lowering the conservative of consistency time Estimation of Upper-Bound, facilitate predetermined time consistency application
In requiring convergence time stringent application.Therefore, to the research of predetermined time consistency tracking problem to real system
Using with important directive function and application prospect.
Summary of the invention
Technical problems to be solved
In order to avoid the shortcomings of the prior art, the present invention propose a kind of predetermined time multi-agent system consistency with
Track control method to facilitate the estimation in the consistency time upper bound and the design of controller, and reduces the guarantor of consistency time Estimate
Keeping property.
Technical solution
A kind of predetermined time multi-agent system consistency tracking and controlling method, it is characterised in that the multiple agent system
System is made of a leader and N number of follower, and the interactive network of N number of follower's composition is non-directed graph Gs, each follow
There is path to be connected between person and leader, the dynamic of i-th of follower are as follows:
Wherein, x1iFor position type state, x2iFor velocity profile state, uiIt is control input；
The dynamic of leader are as follows:
Wherein, x10For position type state, x20For velocity profile state, u0It is the control input of bounded, i.e., in the presence of known to just
Constant λ, so that | u0|≤λ, all follower can not obtain leader control input information, but constant λ to all follower all
It is known；
The consistency Tracking Control Scheme includes the following steps:
Step 1: distributed observer is designed for each follower:
ξ in formulaiAnd ηiI-th of follower's distribution observer state, α, β, λ is observer gain, p and q be meet p <
The positive odd number of q, sig ()α=| |αsign(·)；
Step 2: according to required observation time 2Tb, determine the gain of distribution observer:
λ in formulaminIt (H) is the minimal eigenvalue of matrix H, H=Ls+ B, LsTo scheme GsLaplacian matrix, B=diag
{a10,...,aN0, ai0> 0 expression follower has communication connection to be connected with leader, otherwise ai0=0；Enable observer state
In predetermined time 2TbInside converge to the state of tracking error；
Step 3: defining i-th and follow intelligent body tracking error e1i=x1i-x10, e2i=x2i-x20；It is led in observer
After the status information led, to follow intelligent physical efficiency in preassigned time T i-thc+TdThe track led in interior tracking,
Intelligent body is followed to design non-singular terminal sliding formwork consistency control protocol for i-th:
M in formula, n are normal number, TcFor preassigned stable time, sliding-mode surface siIs defined as:
In formulak1, k2For positive real number, TdIt is predesignated
The stabilization time, ε be small normal number；
Step 4: to make sliding-mode surface and its derivative continuous, control parameter k1, k2It is selected as k1=1+m, k2=-m；To disappear
Except control singularity, control parameter m, n need to meet 0 < m < 1/2,0 < n < 1/2；
Step 5: controller (5) and distributed observer (3) being deployed in i-th of follower, so that all follower
State can be in preassigned time 2Tb+Tc+TdThe track led in interior tracking, i.e., for any time t >=2Tb+Tc+
Td, there is x1i(t)=x10(t), x2i(t)=x20(t) it sets up.
Beneficial effect
There is very high requirement to control precision and consistency time in view of many practical multi-agent systems, the present invention can
The accurate consistency tracking of multi-agent system, and distributed observer/consistency tracking control are realized at the appointed time
The gain of agreement processed can directly be determined that this improves convergence time adjustment and controller design by the specified consistency time
Flexibility facilitates controller design.In addition, proposed method reduces the conservative of convergence time Estimation of Upper-Bound, to drop
The low conservative of controller design.Therefore, the consistency tracking and controlling method proposed is being applied to control precision and receipts
It can show that apparent advantage when holding back the higher system of time requirement.Compared with the existing technology, innovative embodiment of the invention
At following three aspects:
(a), it proposes novel predetermined time consistency Tracking Control Scheme and solves the multi-agent system predetermined time
Tracking problem, the control program proposed include distributed observer and non-singular terminal sliding formwork control agreement, are solved predetermined
Annual distribution formula observes problem and control singular problem.
(b), the consistency time can according to the requirement of convergence time preassign, proposes distribution observer/unanimously
The gain of property tracing control agreement can be determined directly by the specified consistency time.
(c), when existing fixation compared with coherence scheme, method proposed by the invention can obtain lower conservative
Convergence time estimation, this also contribute to reduce controller design conservative.
Detailed description of the invention
Fig. 1 predetermined time consistency Tracking Control Scheme design procedure block diagram
Fig. 2 single connecting rod manipulator multi-agent system interaction topology
Fig. 3 observer state ξiWith tracking error state e1iTime response
Fig. 4 observer state ηiWith tracking error state e2iTime response
Fig. 5 intelligent body state x1iTime response
Fig. 6 intelligent body state x2iTime response
Specific embodiment
Now in conjunction with embodiment, attached drawing, the invention will be further described:
It please refers to shown in Fig. 1 to Fig. 6, the multi-agent system that the present invention considers is by a leader and N number of follower
Composition, the interactive network of N number of follower's composition is non-directed graph Gs, have path phase between each follower and leader
Even, the dynamic of i-th of follower are as follows:
Wherein, x1iFor position type state, x2iFor velocity profile state, uiIt is control input.
The dynamic of leader are as follows:
Wherein, x10For position type state, x20For velocity profile state, u0It is the control input of bounded, i.e., in the presence of known to just
Constant λ, so that | u0|≤λ, all follower can not obtain leader control input information, but constant λ to all follower all
It is known.
The object of the present invention is to provide a kind of predetermined time multi-agent system consistency tracking and controlling methods, to facilitate one
The estimation in the time upper bound of cause property and the design of controller, and reduce the conservative of consistency time Estimate.
In conjunction with Fig. 1, the design cycle of consistency Tracking Control Scheme proposed by the invention the following steps are included:
Step 1: distributed observer is designed for each follower:
ξ in formulaiAnd ηiI-th of follower's distribution observer state, α, β, λ is observer gain, p and q be meet p <
The positive odd number of q, sig ()α=| |αsign(·)。
Step 2: according to required observation time 2Tb, determine the gain of distribution observer
λ in formulaminIt (H) is the minimal eigenvalue of matrix H, H=Ls+ B, LsTo scheme GsLaplacian matrix, B=diag
{a10,...,aN0, ai0> 0 expression follower has communication connection to be connected with leader, otherwise ai0=0.Enable observer state
In predetermined time 2TbInside converge to the state of tracking error.
Step 3: it defines i-th and follows intelligent body tracking error e1i=x1i-x10, e2i=x2i-x20.It is obtained in observer
After the status information of leader, to follow intelligent physical efficiency in preassigned time T i-thc+TdThe rail led in interior tracking
Mark follows intelligent body to design non-singular terminal sliding formwork consistency control protocol for i-th:
M in formula, n are normal number, TcFor preassigned stable time, sliding-mode surface siIs defined as:
In formulak1, k2For positive real number, TdIt is predesignated
The stabilization time, ε is small normal number (such as desirable ε=0.1).
Step 4: to make sliding-mode surface and its derivative continuous, control parameter k1, k2It is selected as k1=1+m, k2=-m. is to disappear
Except control singularity, control parameter m, n need to meet 0 < m < 1/2,0 < n < 1/2.
Step 5: controller (5) and distributed observer (3) are deployed in i-th of follower, so that all follower
State can be in preassigned time 2Tb+Tc+TdThe track led in interior tracking, i.e., for any time t >=2Tb+Tc+
Td, there is x1i(t)=x10(t), x2i(t)=x20(t) it sets up.
Embodiment: single connecting rod manipulator multi-agent system predetermined time consistency tracing control
Single connecting rod arm-and-hand system is an important system of industrial automation, the accuracy of coordinated control and
Rapidity is of great significance to the efficiency and quality that improve execution instruction, develops quickly accurate single connecting rod machinery Handball Association
Control algolithm is adjusted to be of great significance to China's industrial automation level is improved.By taking single connecting rod manipulator multi-agent system as an example
Illustrate the validity of above-mentioned predetermined time consistency tracking and controlling method.Single connecting rod manipulator multi-agent system be by 3 with
It is formed with person's intelligent body and 1 leader's intelligent body, interacts topology as shown in Figure 2.The dynamic of follower's intelligent body can
With description are as follows:
Wherein,qiRespectively indicate the angular acceleration of i-th of connection, angular speed and Angle Position, JiIndicate i-th of company
Meet total rotary inertia with motor, BiIndicate damped coefficient, MiIndicate the gross mass of i-th of connection, g indicates acceleration of gravity, liTable
Show the distance between i-th of connecting joint axis and center of gravity.If control input is designed as
It enablesThen the dynamic of follower's intelligent body can indicate are as follows:
With system (1) expression form having the same.
The dynamic of leader's intelligent body can be described as:
Wherein,And u20It is angular acceleration and the control input of leader of reference locus.Enable x10=q0,Then
(9) there is with (2) identical form.
The initial value of leader's intelligent body is selected as (x10(0),x20(0))=(0,0.1), the initial value choosing of follower's intelligent body
For (x11(0),x21(0),x12(0),x22(0),x13(0),x23(0))=(0.4,0.35,0.2,0.3,0.5,0.25), leader's
U is selected as in control input20=-0.1sin (t), distributed observer and controller parameter are selected as p=5, q=9, Tb=1, α=β=
14.9054, λ=0.1, m=0.3, n=0.4, k1=1.3, k2=-0.3, ε=0.1, Tc=Td=1. distributed observers are estimated
The state of meter and leader's state are as shown in Figure 3-4, by Fig. 3-4 it can be seen that the distributed observer proposed can be in 0.2s
Provide the accurate estimation of tracking error state.Under the controller action proposed multi-agent system state as seen in figs. 5-6,
The control protocol proposed it can be seen from Fig. 5-6 can realize the accurate consistency tracking of multi-agent system in 1.5s.
Simulation result confirms that the tracking of predetermined time consistency may be implemented in proposed control program.
Claims (1)
1. a kind of predetermined time multi-agent system consistency tracking and controlling method, it is characterised in that the multi-agent system
It is made of a leader and N number of follower, the interactive network of N number of follower's composition is non-directed graph Gs,
There is path to be connected between each follower and leader, the dynamic of i-th of follower are as follows:
Wherein, x1iFor position type state, x2iFor velocity profile state, uiIt is control input；
The dynamic of leader are as follows:
Wherein, x10For position type state, x20For velocity profile state, u0It is the control input of bounded, that is, there is known normal number
λ, so that | u0|≤λ, all follower can not obtain the control input information of leader, but constant λ is to all follower
Know；
The consistency Tracking Control Scheme includes the following steps:
Step 1: distributed observer is designed for each follower:
ξ in formulaiAnd ηiIt is i-th of follower's distribution observer state, α, β, λ is observer gain, and p and q meet p < q
Positive odd number, sig ()α=| |αsign(·)；
Step 2: according to required observation time 2Tb, determine the gain of distribution observer:
λ in formulaminIt (H) is the minimal eigenvalue of matrix H, H=Ls+ B, LsTo scheme GsLaplacian matrix, B=diag
{a10,...,aN0, ai0> 0 expression follower has communication connection to be connected with leader, otherwise ai0=0；Enable observer state
In predetermined time 2TbInside converge to the state of tracking error；
Step 3: defining i-th and follow intelligent body tracking error e1i=x1i-x10, e2i=x2i-x20；Obtain leader's in observer
After status information, to follow intelligent physical efficiency in preassigned time T i-thc+TdThe track led in interior tracking is the
I follow intelligent body to design non-singular terminal sliding formwork consistency control protocol:
M in formula, n are normal number, TcFor preassigned stable time, sliding-mode surface siIs defined as:
In formulak1, k2For positive real number, TdIt is preassigned steady
It fixes time, ε is small normal number；
Step 4: to make sliding-mode surface and its derivative continuous, control parameter k1, k2It is selected as k1=1+m, k2=-m；To eliminate control
Singularity, control parameter m, n need to meet 0 < m < 1/2,0 < n < 1/2；
Step 5: controller (5) and distributed observer (3) being deployed in i-th of follower, so that the shape of all follower
State can be in preassigned time 2Tb+Tc+TdThe track led in interior tracking, i.e., for any time t >=2Tb+Tc+Td,
There is x1i(t)=x10(t), x2i(t)=x20(t) it sets up.
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| CN116442212B (en) * | 2023-03-07 | 2023-10-10 | 北京科技大学 | Grouping safety control method for man-in-the-loop multi-mechanical arm system under preset time and precision |
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